Simple photometry question with something going wrong?

[maverick280857]

[EDIT] To be deleted.

[EDIT] To be deleted.

 

[Cthugha]

$$\frac{1}{4\pi x^{2}}\times\pi\frac{d^2}{4}$$

Therefore the fraction of detected gamma rays is 50% of this fraction

I do not think your reasoning is correct here. You correctly calculate the ratio of the detector surface compared to the total surface of a sphere with diameter x, which is the fraction of detected gamma rays. If the point source is positioned directly in front of the detector, it is a good approximation to consider the detector surface to be as large as half of the total sphere with small diameter. Therefore 50% of the gamma rays will be detected and the 50% emitted in the other direction will not be detected. If you multiply this factor 0.5 again to the ratio of detected gamma rays you calculated before, you consider this factor twice and get a wrong result - unless I misunderstood the problem and the 50% are a measure of detector efficiency, but I do not think so.

 

[maverick280857]

Thank you for replying.

The 50% controls the fraction of the solid angle over which the detector gets the flux...so its 2*pi*(d/2)^2/(4*pi*x^2) = (d/4x)^2.